Game Theory (Part 18)

We’re talking about zero-sum 2-player normal form games. Last time we saw that in a Nash equilibrium for a game like this, both players must use a maximin strategy. Now let’s try to prove the converse!

In other words: let’s try to prove that if both players use a maximin strategy, the result is a Nash equilibrium.

Today we’ll only prove this is true if a certain equation holds. It’s the cool-looking equation we saw last time:

Last time we showed this cool-looking equation is true whenever our game has a Nash equilibrium. In fact, this equation is always true. In other words: it’s true for any zero-sum two-player normal form game. The reason is that any such game has a Nash equilibrium. But we haven’t showed that yet.

How To Write Math Here:

You need the word 'latex' right after the first dollar sign, and it needs a space after it. Double dollar signs don't work, and other limitations apply, some described here. You can't preview comments here, but I'm happy to fix errors.